Parallelogram ABCD is a rectangle.

1 answer:

8 0

The correct answer is y = 11

because:
2y + 7 = 3y − 4
−y + 7 =−4

Subtract 7 from both sides.
−y + 7 − 7 = − 4 − 7
−y = −11

Divide both sides by -1.
y = 11

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WORTH 49 POINTS! How far away is -5 to |-5|?

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|-5| is equivalent to 5, since that is how far -5 is from 0.

So, the question is simplified to: How far away is -5 from 5?

We get 5-(-5)=10.

Remember, absolute value is always positive (expect for 0) and the distance between two numbers is always positive (expect for 0).

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3 years ago

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The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A

Maksim231197 [3]

Answer:

The 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =65$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=11-1=10$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,10)".And we see that $t_{\alpha/2}=1.81$